{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,19]],"date-time":"2026-02-19T15:10:48Z","timestamp":1771513848388,"version":"3.50.1"},"reference-count":42,"publisher":"Emerald","issue":"3","license":[{"start":{"date-parts":[[2021,4,8]],"date-time":"2021-04-08T00:00:00Z","timestamp":1617840000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.emerald.com\/insight\/site-policies"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IR"],"published-print":{"date-parts":[[2021,8,3]]},"abstract":"<jats:sec>\n<jats:title content-type=\"abstract-subheading\">Purpose<\/jats:title>\n<jats:p>With the increasing demand for surveillance and smart transportation, drone technology has become the center of attraction for robotics researchers. This study aims to introduce a new path planning approach to drone navigation based on topology in an uncertain environment. The main objective of this study is to use the Ricci flow evolution equation of metric and curvature tensor over angular Riemannian metric, and manifold for achieving navigational goals such as path length optimization at the minimum required time, collision-free obstacle avoidance in static and dynamic environments and reaching to the static and dynamic goals. The proposed navigational controller performs linearly and nonlinearly both with reduced error-based objective function by Riemannian metric and scalar curvature, respectively.<\/jats:p>\n<\/jats:sec>\n<jats:sec>\n<jats:title content-type=\"abstract-subheading\">Design\/methodology\/approach<\/jats:title>\n<jats:p>Topology and manifolds application-based methodology establishes the resultant drone. The trajectory planning and its optimization are controlled by the system of evolution equation over Ricci flow entropy. The navigation follows the Riemannian metric-based optimal path with an angular trajectory in the range from 0\u00b0 to 360\u00b0. The obstacle avoidance in static and dynamic environments is controlled by the metric tensor and curvature tensor, respectively. The in-house drone is developed and coded using C++. For comparison of the real-time results and simulation results in static and dynamic environments, the simulation study has been conducted using MATLAB software. The proposed controller follows the topological programming constituted with manifold-based objective function and Riemannian metric, and scalar curvature-based constraints for linear and nonlinear navigation, respectively.<\/jats:p>\n<\/jats:sec>\n<jats:sec>\n<jats:title content-type=\"abstract-subheading\">Findings<\/jats:title>\n<jats:p>This proposed study demonstrates the possibility to develop the new topology-based efficient path planning approach for navigation of drone and provides a unique way to develop an innovative system having characteristics of static and dynamic obstacle avoidance and moving goal chasing in an uncertain environment. From the results obtained in the simulation and real-time environments, satisfactory agreements have been seen in terms of navigational parameters with the minimum error that justifies the significant working of the proposed controller. Additionally, the comparison of the proposed navigational controller with the other artificial intelligent controllers reveals performance improvement.<\/jats:p>\n<\/jats:sec>\n<jats:sec>\n<jats:title content-type=\"abstract-subheading\">Originality\/value<\/jats:title>\n<jats:p>In this study, a new topological controller has been proposed for drone navigation. The topological drone navigation comprises the effective speed control and collision-free decisions corresponding to the Ricci flow equation and Ricci curvature over the Riemannian metric, respectively.<\/jats:p>\n<\/jats:sec>","DOI":"10.1108\/ir-10-2020-0218","type":"journal-article","created":{"date-parts":[[2021,4,6]],"date-time":"2021-04-06T07:44:56Z","timestamp":1617695096000},"page":"423-441","source":"Crossref","is-referenced-by-count":12,"title":["Topological drone navigation in uncertain environment"],"prefix":"10.1108","volume":"48","author":[{"given":"Bhumeshwar","family":"Patle","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shyh-Leh","family":"Chen","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Brijesh","family":"Patel","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sunil Kumar","family":"Kashyap","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sudarshan","family":"Sanap","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"140","published-online":{"date-parts":[[2021,4,8]]},"reference":[{"key":"key2021080209262853900_ref001","first-page":"4907","article-title":"A topological approach of path planning for autonomous robot navigation in dynamic environments","volume-title":"IEEE\/RSJ International Conference on Intelligent Robots and Systems","year":"2009"},{"key":"key2021080209262853900_ref002","volume-title":"The Ricci Flow in Riemannian Geometry: A Complete Proof of the Differentiable 1\/4-Pinching Sphere Theorem","year":"2010"},{"issue":"5","key":"key2021080209262853900_ref003","doi-asserted-by":"crossref","first-page":"803","DOI":"10.1017\/S0263574713001070","article-title":"Topological simultaneous localization and mapping: a survey","volume":"32","year":"2014","journal-title":"Robotica"},{"key":"key2021080209262853900_ref004","doi-asserted-by":"crossref","first-page":"132","DOI":"10.1016\/j.comcom.2020.07.019","article-title":"A staged adaptive firefly algorithm for UAV charging planning in wireless sensor networks","volume":"161","year":"2020","journal-title":"Computer Communications"},{"issue":"2","key":"key2021080209262853900_ref005","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1109\/70.928558","article-title":"Topological simultaneous localization and mapping (SLAM): toward exact localization without explicit localization","volume":"17","year":"2001","journal-title":"IEEE Transactions on Robotics and Automation"},{"key":"key2021080209262853900_ref006","volume-title":"The Ricci Flow: techniques and Applications","year":"2007"},{"issue":"3","key":"key2021080209262853900_ref007","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1109\/JRA.1987.1087096","article-title":"Sonar-based real-world mapping and navigation","volume":"3","year":"1987","journal-title":"IEEE Journal on Robotics and Automation"},{"issue":"1","key":"key2021080209262853900_ref008","doi-asserted-by":"crossref","first-page":"24","DOI":"10.1109\/MPRV.2017.11","article-title":"Help from the sky: leveraging UAVs for disaster management","volume":"16","year":"2017","journal-title":"IEEE Pervasive Computing"},{"key":"key2021080209262853900_ref009","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1090\/conm\/438\/08447","article-title":"Symmetric motion planning, topology and robotics","volume":"438","year":"2007","journal-title":"Contemporary Mathematics"},{"issue":"4","key":"key2021080209262853900_ref010","doi-asserted-by":"crossref","first-page":"243","DOI":"10.1016\/S1389-0417(03)00008-1","article-title":"Map-based navigation in mobile robots: i. a review of localization strategies","volume":"4","year":"2003","journal-title":"Cognitive Systems Research"},{"key":"key2021080209262853900_ref011","first-page":"193","volume-title":"Topological Complexity of Motion Planning and Massey Products, Algebraic Topology-Old and New","year":"2009"},{"issue":"2","key":"key2021080209262853900_ref012","doi-asserted-by":"crossref","first-page":"4019002","DOI":"10.1061\/(ASCE)IS.1943-555X.0000464","article-title":"Applications of UAVs in civil infrastructure","volume":"25","year":"2019","journal-title":"Journal of Infrastructure Systems"},{"issue":"1","key":"key2021080209262853900_ref013","first-page":"90","article-title":"A fully autonomous indoor quadrotor","volume":"28","year":"2011","journal-title":"IEEE Transactions on Robotics"},{"key":"key2021080209262853900_ref014","first-page":"7","article-title":"Formation of singularities in the ricci flow","volume":"2","year":"1995","journal-title":"Surveys in Diff. 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